Vibration-insensitive phase-shifting interferometry based on frequency domain analysis

An algorithm was proposed to deal with the phase-shifting error and contrast variation in a Phase-shifting Interferometry (PSI) under vibration. The algorithm detected phase shifts and contrast variation by analyzing the spectra of spatial-carrier interferograms firstly. Then the phase shifts were used as priori information to retrieve the wavefront phase from least-square equation with contrast compensation. To deal with interferograms with non-rectangular aperture, a mask with soft border was constructed and data extrapolation was avoided. The effectiveness of the proposed algorithm was validated by simulations and experiments. The simulation results show the proposed method can detect the phase shifts and contrast variation in high accuracy and can compensate effectively phase retrieval errors caused by contrast variation. The practicability of the algorithm was verified under a simple harmonic vibration with a frequency of 9 Hz and an amplitude of 0.5 μm. The measurement under vibration demonstrates that the retrieval error of a flat surface is less than 0.015 waves (PV value). The algorithm provides a low-cost approach to application of PSI to field measurement under vibration without modification of the hardware of interferometers. ©, 2015, Chinese Academy of Sciences. All right reserved.